Hum, simple I'm sure but perhaps calculating APR is not quite that simple;
you have to factor in loan expenses (that's why APR is not the same as
interest rate).
I think it is something like:
P' = (P+E)I(1+i)^n/(1+i)^n
Then you solve for APR with the nonlinear function which is something like:
((a(1+a)^n)(P'/P))/((1+a)^n1) = 0
Where a=ARR/12
Calculating P' is straightforward. Solving for a is where I'm not clear,
plus I'm not certain of the math above.
Dave
Original Message
From: Bear Giles [mailto:bgiles@coyotesong.com]
Sent: Saturday, August 16, 2008 3:40 PM
To: Commons Users List
Subject: Re: commonsmath usage to calculate APR?
There are closedform expressions for that, although I don't have them
off the top of my head. Something like
m = P / (1  i)^n
or maybe
m = P / ((1 + i)^n  1)
where m is monthly payment, P is principal, i is monthly interest, n is
number of months. It's definitely not very complex for a simple
fixedterm, fixedrate loan.
Bear
David Hoffer wrote:
> My usage is for USA only at this point.
>
> I have inputs of loanAmount, monthlyInterestRate, numberMonths, loanFees;
so
> this would be for fixed monthly payments.
>
> I understand that commonsmath doesn't have specific finance methods
however
> I think the APR formula is a nonlinear equation that I was hoping
> commonsmath could help solve.
>
> Dave
>
> Original Message
> From: Luc Maisonobe [mailto:Luc.Maisonobe@free.fr]
> Sent: Saturday, August 16, 2008 2:45 PM
> To: Commons Users List
> Subject: Re: commonsmath usage to calculate APR?
>
> David Hoffer a écrit :
>
>> Can anyone point me to an example of how to use commonsmath to calculate
>> APR (Annual Percentage Rate)?
>>
>
> There are no specific finance related algorithm in commonsmath.
>
>
>> I think this is solvable using either the NewtonSolver or BisectionSolver
>> but I am not sure how to accomplish this. Perhaps a different way is
>> better.
>>
>
> I think so, but it depends on what you really need. APR computation
> seems to be slightly different depending on local regulations (for
> example USA or EU). It also depends on the assumptions you do and the
> input data. For example you can compute it one way for fixed monthly
> payments and another way for varying monthly payments.
>
>
>> Any help would be greatly appreciated.
>>
>
> Could you explain your needs more precisely ?
>
> Luc
>

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